ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps 4 : 3
                     ⟩ : : 8 : x
Days    1 : 2
4 × 1 × x = 3 × 2 × 8
x = 12
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Shortly:
Pumps 4 : 3 and Days    1 : 2
by combining, we get, 
4 × 1 × x = 3 × 2 × 8
x = 12

After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x
125x = 150 × 35
x = 42

Let the total number of men be x
Work done = 1/3
Remaining work = (1 - 1/3) = 2/3
More work, More men (Direct proportion)
More days, Less men (Indirect proportion)
Work 1/3 : 2/3
Days 25 : 20
1/3 × 25 × x = 2/3 × 20 × 20
x = 32
∴ More men to be employed = (32 - 20) = 12

Cost of 21 pencils and 9 clippers = Tk. 819
That means, cost of 3(7 pencils and 3 clippers) = Tk. 819
Cost of (7 pencils and 3 clippers) = Tk.  819/3
 = Tk. 273

Cost of 8 fan's and 14 oven's is Tk. 36520
Cost of 4 fan's and 7 oven's is Tk. 36520/2
  = Tk.18260
Cost of 12 fan's and 21 oven's is
= 18260 × 3
= Tk. 54780

Let the required number of rounds be x
More radius, Less rounds (Indirect proportion)
20 : 14 :: 70 : x
⇒ 20x = 14 × 70
⇒ x = 49

Let the required number of days be x
7 men = 10 women
(14 men and 20 women) = (20 + 20) women = 40 women
More length, More days (Direct proportion)
More women, Less days (Indirect proportion)
Length 100 : 600
                          ⟩ :: 10 : x
 Women 40 : 10
100 × 40 × x = 600 × 10 × 10
x = 15

Let the required number of days be x
Less people, More days (Indirect proportion)
Less quantity, Less days ( Direct proportion)
     People 35 : 50
                            ⟩ :: 30 : x
Quantity 350 : 50
⇒ 35 × 350 × x = 50 × 50 × 30 
⇒ x = 300/49

Let the required time be x seconds
Then,
More metres, More time (direct proportion)
∴ 0.128 : 25 :: 1 : x
x = 195.31
∴ Required time =195 seconds (approx)

cm on the map represents 1450 km
∴ 1 cm on the map represents (1450/5 km = 290 km
Hence,
the scale is 1 cm : 290 km
= 1cm : 29 × 10⁶cm
= 1 : 29 × 10⁶

(A+B)'s one day's work = 1/3 part
(A+B) works 2 days together = 2/3 part
Remaining work = 1−2/3 = 1/3 part
1/3 part of work is completed by A in two days
Hence, one day's work of A = 1/6
Then, one day's work of B = 1/3−1/6 = 1/6
So, B alone can complete the whole work in 6 days.

% Cistern is filled by 1st pipe in one minute
= 100/20
 = 5%
% Cistern is filled by 2nd pipe in one minute
= 100/30
 = 3.33%
% cistern filled by 1st and 2nd pipes in one minute = 8.33%

According to question,
Cistern is totally filled by 2nd pipe in last 10 minute.
That means 2nd pipe filled 33.3% of the cistern in last 10 minute and 66.66% of cistern is filled by 1st and 2nd pipe together in = 66.66/8.33 = 8 minutes
Thus, after 8 minute, 1st pipe must be turned off.

 

Let capacity of the tank = x gallons;
Part of the tank filled in 1 minute = x/24 + x/40 - 30
x/24 + x/40 - 30 = x/60
x = 600 gallons

P can fill cistern in 12 minutes
P fills cistern in 1 minute = 1/12 part

Q can fill cistern in 15 minutes
Q fills cistern in 1 minute = 1/15 part
P and Q together can fill cistern in 1 minute,
=1/12 + 1/15 = 9/60 part
So, they can together fill cistern in 3 minute,
= 3 × 9/60 = 9/20 part
Rest Cistern
= 1− 9/20
  = 11/20 part
cistern must be filled by Q in (11/20) ÷ (1/15)
= 8 minutes 15 seconds

Let the pipes fill the tank in x minutes.
Part of tank filled by pipes A and B in one minute:
1/36 Part of the tank filled by pipe A in 1 minute = 1/36−1/x
According to the question,
30×1/x + 40(1/36−1/x) = 1
⇒30/x + 40/36 − 40/x = 1
⇒30/x + 10/9 − 40/x = 1
⇒10/x = 1/9
Hence, x = 90 minutes.

Ratio of their daily wages = 5 : 6 : 4
Total wage = Tk. 1800
6 × 5x + 4 × 6x + 4 × 9x = 1800 [As A, B, C works for 6, 4, 9 days respectively]
Or, 90x = 1800
Or, x = 1800/90

Total amount of A
= 1800 × 30/90
   = Tk. 600

Man = 3 boy
Daily wages for them = 800/5
 = 160
4 boy (1 man + 1 boy) = 160
4 boy = 160
Or, boy = Tk. 40

Number of page copied by Subhash and Prakash in 1 hour
= 300/40
  = 7.5 pages;

Subhash copied pages in one hour
= 50/10
 = 5 pages

Hence, Prakash copied pages in one hour
= 7.5 - 5
= 2.5

Thus, Prakash can copied 30 pages in
= 30/2.5
 = 12 hours

1200 × 45 = 1000 × x
Hence, x = 54 days